Molecular dynamics/xfem coupling by a three-dimensional extended bridging domain with applications to dynamic brittle fracture

We propose a method to couple a three-dimensional continuum domain to a molecular dynamics domain to simulate propagating cracks in dynamics. The continuum domain is treated by an extended finite element method to handle the discontinuities. The coupling is based on the bridging domain method, which blends the continuum and atomistic energies. The Lennard-Jones potential is used to model the interactions in the atomistic domain, and the Cauchy-Born rule is used to compute the material behavior in the continuum domain. To our knowledge, it is the first time that a three dimensional extended bridging domain method is reported. To show the suitability of the proposed method, a threedimensional crack problem with an atomistic region around the crack front is solved. The results show that the method is capable of handling crack propagation and dislocation nucleation.